Sample-Based SMPC for Tracking Control of Fixed-Wing UAV

Abstract

In this paper, a guidance and tracking control strategy for fixed-wing Unmanned Aerial Vehicle (UAV) autopilots is presented. The proposed control exploits recent results on sample-based stochastic Model Predictive Control, which allow coping in a computationally efficient way with both parametric uncertainty and additive random noise. Different application scenarios are discussed, and the implementability of the proposed approach are demonstrated through software-in-the-loop simulations. The capability of guaranteeing probabilistic robust satisfaction of the constraint specifications represents a key-feature of the proposed scheme, allowing real-time tracking of the designed trajectory with guarantees in terms of maximal deviation with respect to the planned one. The presented simulations show the effectiveness of the proposed control scheme. *This work was not supported by any organization 1 M. Mammarella is with the

Chance constrained sets approximation: A probabilistic scaling approach -- EXTENDED VERSION

“…Remark 1 (Joint vs. individual CCs) The constraint θ ∈ X ε , with X ε defined in (6), describes a joint chance constraint. That is, it requires that the joint probability of satisfying the inequality constraint…”

“…In several applications, including engineering and finance, where uncertainties in price, demand, supply, currency exchange rate, recycle and feed rate, and demographic condition are common, it is acceptable, up to a certain safe level, to relax the inherent conservativeness of robust constraints enforcing probabilistic constraints. More recently, the method has been used also in unmanned autonomous vehicle navigation [6,7] as well as optimal power flow [8,9].…”

Distributed stochastic MPC for linear systems with probabilistic constraints and quantisation

“…However, centralised MPC was utilised in these works and probabilistic constraints were not included in the MPC design. Up to date, there are three major methods for single‐system SMPC, such as stochastic tube methods [10, 11], affine parameterisation methods [12, 13] and sample‐based methods [14, 15]. The stochastic tube method is more flexible for distributed systems compared with the other two methods, this method was used in [10] to deal with the probabilistic constraints, and a necessary and sufficient condition was proposed to ensure the satisfaction of the probabilistic constraints.…”

“…The stochastic tube method is more flexible for distributed systems compared with the other two methods, this method was used in [10] to deal with the probabilistic constraints, and a necessary and sufficient condition was proposed to ensure the satisfaction of the probabilistic constraints. An SMPC strategy similar to nominal MPC was presented in [11] to deal with the probabilistic constraints, the cross‐sectional shape of a tube contains predicted trajectories was fixed but the centre and scale are allowed to vary. However, the results of [10, 11] are limited to single system case, therefore, additional techniques are needed to generalise these results to distributed systems.…”

“…An SMPC strategy similar to nominal MPC was presented in [11] to deal with the probabilistic constraints, the cross‐sectional shape of a tube contains predicted trajectories was fixed but the centre and scale are allowed to vary. However, the results of [10, 11] are limited to single system case, therefore, additional techniques are needed to generalise these results to distributed systems.…”